Only 9% of likely voters in New Hampshire "definitely" want President Biden to run again, while 20% said he should "probably" run, according to a poll of likely voters in the state that hosts the first primary in presidential elections.

The number of voters who definitely do not want Biden to run again increased from 43% in 2021 to 52% in 2022, according to the University of New Hampshire Survey Center poll released Wednesday. 

Among likely Democratic voters, just 54% said Biden should run again — a steep drop-off from the 74% of self-identified Democrats who said they wanted Biden to seek re-election in University of New Hampshire's 2021 survey.

Vice President Kamala Harris' approval rating in New Hampshire is well below President Biden's, according to a Wednesday poll measuring support for potential 2024 candidates.

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Joe Biden Harris Kamala

President Biden and Vice President Kamala Harris. (Getty Images)

Harris had 23% favorability in the University of New Hampshire poll, compared to Biden's 23%, but the amount of likely Democratic primary voters who viewed the vice president unfavorably was substantially higher. Sixty-four percent of respondents view Harris unfavorably as a potential 2024 Democratic presidential nominee, compared to 56% who viewed Biden unfavorably.

Biden's net unfavorability of negative 30 percentage points is tied for the lowest ever, which was set in May 2020, a few months before he won the Democratic nomination for president.

A nationwide Fox News poll conducted earlier in June found that a Harris is unpopular among likely voters, with 39% viewing her favorably and 56% unfavorably.

Kamala Harris

Vice President Kamala Harris delivers remarks, and President Biden signs an executive order on project labor agreements (Kyle Mazza/Anadolu Agency via Getty Images)

Speculation about selecting a Democratic nominee other than Biden has increased recently amid the president's disappointing approval ratings, concerns about his age and the potential for a disastrous midterm cycle for Democrats. 

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The University of New Hampshire's survey also covered potential Republican presidential nominees, and voters had a more favorable view of Florida Gov. Ron DeSantis than former President Trump.

Among likely Republican primary voters, 39% said they would support the first-term Florida governor, and 37% said they would back the former president. Respondents were provided a list of potential contenders for the 2024 GOP presidential nomination, and DeSantis' margin was well within the survey’s sampling error.

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Ron DeSantis shakes President Donald Trump's hand.

Ron DeSantis with Donald Trump. (Getty Images)

New Hampshire holds the first primary in the presidential nominating cycle and is a perennial battleground state. Trump lost the state’s four electoral votes to Democratic nominee Hillary Clinton in 2016 by a razor-thin margin, and Biden won the state by 7 points in the 2020 election.

The poll indicates Biden would top Trump 50%-43% in New Hampshire in a hypothetical 2024 general election matchup but shows DeSantis edging out Biden 47%-46%.

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The UNH Survey Center poll was conducted June 16-20, with 845 likely 2024 general election voters — including 318 likely GOP primary voters — questioned online. The survey’s overall sampling error is plus or minus 3.4 percentage points, with a sampling error of plus or minus 5.5 percentage points for likely GOP primary voters.

Fox News' Paul Steinhauser contributed to this report